Matrix Embedding With Pseudorandom Coefficient Selection and Error Correction for Robust and Secure Steganography

Abstract

In matrix embedding (ME)-based steganography, the host coefficients are minimally perturbed such that the transmitted bits fall in a coset of a linear code, with the syndrome conveying the hidden bits. The corresponding embedding distortion and vulnerability to steganalysis are significantly less than that of conventional quantization index modulation (QIM)-based hiding. However, ME is less robust to attacks, with a single host bit error leading to multiple decoding errors for the hidden bits. In this paper, we employ the ME-RA scheme, a combination of ME-based hiding with powerful repeat accumulate (RA) codes for error correction, to address this problem. A key contribution of this paper is to compute log likelihood ratios for RA decoding, taking into account the many-to-one mapping between the host coefficients and an encoded bit, for ME. To reduce detectability, we hide in randomized blocks, as in the recently proposed Yet Another Steganographic Scheme (YASS), replacing the QIM-based embedding in YASS by the proposed ME-RA scheme. We also show that the embedding performance can be improved by employing punctured RA codes. Through experiments based on a couple of thousand images, we show that for the same embedded data rate and a moderate attack level, the proposed ME-based method results in a lower detection rate than that obtained for QIM-based YASS.